arXiv subjects

Masaaki Fujii

Publications and source records attributed to Masaaki Fujii.

At least 37 records · Page 2Linked to original sources

arXiv2015

Optimal Position Management for a Market Maker with Stochastic Price Impacts

This paper deals with an optimal position management problem for a market maker who has to face uncertain customer order flows in an illiquid market, where the market maker's continuous trading incurs a stochastic linear price impact. Although the execution timing is uncertain, the market maker can also ask its OTC counterparties to transact a block trade without causing a direct price impact. We adopt quite generic stochastic processes of the securities, order flows, price impacts, quadratic penalties as well as security borrowing/lending rates. The solution of the market maker's optimal position-management strategy is represented by a stochastic Hamilton-Jacobi-Bellman equation, which can be decomposed into three (one non-linear and two linear) backward stochastic differential equations (BSDEs). We provide the verification using the standard BSDE techniques for a single security case. For a multiple-security case, we make use of the connection of the non-linear BSDE to a special type of backward stochastic Riccati differential equation (BSRDE) whose properties were studied by Bismut(1976). We also propose a perturbative approximation scheme for the resultant BSRDE, which only requires a system of linear ODEs to be solved at each expansion order. Its justification and the convergence rate are also given.

q-fin.PR↗

arXiv2014

A Polynomial Scheme of Asymptotic Expansion for Backward SDEs and Option pricing

A new asymptotic expansion scheme for backward SDEs (BSDEs) is proposed.The perturbation parameter is introduced just to scale the forward stochastic variables within a BSDE. In contrast to the standard small-diffusion asymptotic expansion method, the dynamics of variables given by the forward SDEs is treated exactly. Although it requires a special form of the quadratic covariation terms of the continuous part, it allows rather generic drift as well as jump components to exist. The resultant approximation is given by a polynomial function in terms of the unperturbed forward variables whose coefficients are uniquely specified by the solution of the recursive system of linear ODEs. Applications to a jump-extended Heston and lambda-SABR models for European contingent claims, as well as the utility-optimization problem in the presence of a terminal liability are discussed.

q-fin.CP↗

arXiv2014

Optimal Hedging for Fund & Insurance Managers with Partially Observable Investment Flows

All the financial practitioners are working in incomplete markets full of unhedgeable risk-factors. Making the situation worse, they are only equipped with the imperfect information on the relevant processes. In addition to the market risk, fund and insurance managers have to be prepared for sudden and possibly contagious changes in the investment flows from their clients so that they can avoid the over- as well as under-hedging. In this work, the prices of securities, the occurrences of insured events and (possibly a network of) the investment flows are used to infer their drifts and intensities by a stochastic filtering technique. We utilize the inferred information to provide the optimal hedging strategy based on the mean-variance (or quadratic) risk criterion. A BSDE approach allows a systematic derivation of the optimal strategy, which is shown to be implementable by a set of simple ODEs and the standard Monte Carlo simulation. The presented framework may also be useful for manufactures and energy firms to install an efficient overlay of dynamic hedging by financial derivatives to minimize the costs.

q-fin.CP↗

arXiv2014

Unusual behavior in the first excited state lifetime of catechol

We are presenting vibrationally selective pump-probe measurements of the first electronic excited-state (pp*) lifetime of jet-cooled neutral catechol (1,2-dihydroxybenzene). The lifetime of the 0-0 transition is very short (7 ps) as rationalized by the small pp*/psigma* gap calculated. However the lifetimes implying higher out-of-plane vibrational levels are longer (~11 ps). This emphasizes the role of the out-of-plane vibration in the pp*/psigma* coupling not only in its nature but also in the number of quanta

physics.atm-clus↗

arXiv2013

Making Mean-Variance Hedging Implementable in a Partially Observable Market

The mean-variance hedging (MVH) problem is studied in a partially observable market where the drift processes can only be inferred through the observation of asset or index processes. Although most of the literatures treat the MVH problem by the duality method, here we study a system consisting of three BSDEs derived by Mania and Tevzadze (2003) and Mania et.al.(2008) and try to provide more explicit expressions directly implementable by practitioners. Under the Bayesian and Kalman-Bucy frameworks, we find that a relevant BSDE yields a semi-closed solution via a simple set of ODEs which allow a quick numerical evaluation. This renders remaining problems equivalent to solving European contingent claims under a new forward measure, and it is straightforward to obtain a forward looking non-sequential Monte Carlo simulation scheme. We also give a special example where the hedging position is available in a semi-closed form. For more generic setups, we provide explicit expressions of approximate hedging portfolio by an asymptotic expansion. These analytic expressions not only allow the hedgers to update the hedging positions in real time but also make a direct analysis of the terminal distribution of the hedged portfolio feasible by standard Monte Carlo simulation.

q-fin.CP↗

arXiv2013

Momentum-Space Approach to Asymptotic Expansion for Stochastic Filtering

This paper develops an asymptotic expansion technique in momentum space for stochastic filtering. It is shown that Fourier transformation combined with a polynomial-function approximation of the nonlinear terms gives a closed recursive system of ordinary differential equations (ODEs) for the relevant conditional distribution. Thanks to the simplicity of the ODE system, higher order calculation can be performed easily. Furthermore, solving ODEs sequentially with small sub-periods with updated initial conditions makes it possible to implement a substepping method for asymptotic expansion in a numerically efficient way. This is found to improve the performance significantly where otherwise the approximation fails badly. The method is expected to provide a useful tool for more realistic financial modeling with unobserved parameters, and also for problems involving nonlinear measure-valued processes.

q-fin.CP↗

arXiv2012

An FBSDE Approach to American Option Pricing with an Interacting Particle Method

In the paper, we propose a new calculation scheme for American options in the framework of a forward backward stochastic differential equation (FBSDE). The well-known decomposition of an American option price with that of a European option of the same maturity and the remaining early exercise premium can be cast into the form of a decoupled non-linear FBSDE. We numerically solve the FBSDE by applying an interacting particle method recently proposed by Fujii and Takahashi (2012d), which allows one to perform a Monte Carlo simulation in a fully forward-looking manner. We perform the fourth-order analysis for the Black-Scholes (BS) model and the third-order analysis for the Heston model. The comparison to those obtained from existing tree algorithms shows the effectiveness of the particle method.

q-fin.CP↗

arXiv2012

Perturbative Expansion of FBSDE in an Incomplete Market with Stochastic Volatility

In this work, we apply our newly proposed perturbative expansion technique to a quadratic growth FBSDE appearing in an incomplete market with stochastic volatility that is not perfectly hedgeable. By combining standard asymptotic expansion technique for the underlying volatility process, we derive explicit expression for the solution of the FBSDE up to the third order of volatility-of-volatility, which can be directly translated into the optimal investment strategy. We compare our approximation with the exact solution, which is known to be derived by the Cole-Hopf transformation in this popular setup. The result is very encouraging and shows good accuracy of the approximation up to quite long maturities. Since our new methodology can be extended straightforwardly to multi-dimensional setups, we expect it will open real possibilities to obtain explicit optimal portfolios or hedging strategies under realistic assumptions.

q-fin.CP↗

arXiv2012

Perturbative Expansion Technique for Non-linear FBSDEs with Interacting Particle Method

In this paper, we propose an efficient Monte Carlo implementation of non-linear FBSDEs as a system of interacting particles inspired by the ideas of branching diffusion method. It will be particularly useful to investigate large and complex systems, and hence it is a good complement of our previous work presenting an analytical perturbation procedure for generic non-linear FBSDEs. There appear multiple species of particles, where the first one follows the diffusion of the original underlying state, and the others the Malliavin derivatives with a grading structure. The number of branching points are capped by the order of perturbation, which is expected to make the scheme less numerically intensive. The proposed method can be applied to semi-linear problems, such as American and Bermudan options, Credit Value Adjustment (CVA), and even fully non-linear issues, such as the optimal portfolio problems in incomplete and/or constrained markets, feedbacks from large investors, and also the analysis of various risk measures.

q-fin.CP↗

arXiv2012

Analytical Approximation for Non-linear FBSDEs with Perturbation Scheme

In this work, we have presented a simple analytical approximation scheme for generic non-linear FBSDEs. By treating the interested system as the linear decoupled FBSDE perturbed with non-linear generator and feedback terms, we have shown that it is possible to carry out a recursive approximation to an arbitrarily higher order, where the required calculations in each order are equivalent to those for standard European contingent claims. We have also applied the perturbative method to the PDE framework following the so-called Four Step Scheme. The method is found to render the original non-linear PDE into a series of standard parabolic linear PDEs. Due to the equivalence of the two approaches, it is also possible to derive approximate analytic solution for the non-linear PDE by applying the asymptotic expansion to the corresponding probabilistic model. Two simple examples are provided to demonstrate how the perturbation works and show its accuracy relative to known numerical techniques. The method presented in this paper may be useful for various important problems which have eluded analytical treatment so far.

q-fin.CP↗

arXiv2011

Derivative Pricing under Asymmetric and Imperfect Collateralization and CVA

The importance of collateralization through the change of funding cost is now well recognized among practitioners. In this article, we have extended the previous studies of collateralized derivative pricing to more generic situation, that is asymmetric and imperfect collateralization with the associated counter party credit risk. By introducing the collateral coverage ratio, our framework can handle these issues in an unified manner. Although the resultant pricing formula becomes non-linear FBSDE and cannot be solve exactly, the fist order approximation is provided using Gateaux derivative. We have shown that it allows us to decompose the price of generic contract into three parts: market benchmark, bilateral credit value adjustment (CVA), and the collateral cost adjustment (CCA) independent from the credit risk. We have studied each term closely, and demonstrated the significant impact of asymmetric collateralization through CCA using the numerical examples.

q-fin.PR↗

arXiv2011

Clean Valuation Framework for the USD Silo

In the forthcoming ISDA Standard Credit Support Annex (SCSA), the trades denominated in non-G5 currencies as well as those include multiple currencies are expected to be allocated to the USD silo, where the contracts are collateralized by USD cash, or a different currency with an appropriate interest rate overlay to achieve the same economic effects. In this paper, we have presented a simple generic valuation framework for the clean price under the USD silo with the the detailed procedures for the initial term structure construction. We have also shown that Cross Currency Swap (CCS) basis spread can be expressed as a difference between two swap rates.

q-fin.PR↗

arXiv2011

Collateralized CDS and Default Dependence

In this paper, we have studied the pricing of a continuously collateralized CDS. We have made use of the "survival measure" to derive the pricing formula in a straightforward way. As a result, we have found that there exists irremovable trace of the counter party as well as the investor in the price of CDS through their default dependence even under the perfect collateralization, although the hazard rates of the two parties are totally absent from the pricing formula. As an important implication, we have also studied the situation where the investor enters an offsetting back-to-back trade with another counter party. We have provided simple numerical examples to demonstrate the change of a fair CDS premium according to the strength of default dependence among the relevant names, and then discussed its possible implications for the risk management of the central counter parties.

q-fin.PR↗

arXiv2003

Neutralino Dark Matter from MSSM Flat Directions in light of WMAP Result

The minimal supersymmetric standard model (MSSM) has a truly supersymmetric way to explain both the baryon asymmetry and cold dark matter in the present Universe, that is, ``Affleck-Dine baryo/DM-genesis.'' The associated late-time decay of Q-balls directly connects the origins of the baryon asymmetry and dark matter, and also predicts a specific nature of the LSP. In this paper, we investigate the prospects for indirect detection of these dark matter candidates observing high energy neutrino flux from the Sun, and hard positron flux from the halo. We also update the previous analysis of the direct detection in hep-ph/0205044 by implementing the recent result from WMAP satellite.

hep-ph↗

arXiv2002

Non-thermal Dark Matter from Affleck-Dine Baryogenesis

In this talk we discuss the origin and nature of the dark matter in the Affleck-Dine (AD) baryogenesis. The AD baryogenesis via most of the flat directions predict formations of large Q-balls, and a great number of the lightest supersymmetric particles (LSPs) are produced nonthermally via the late-time decays of these Q-balls. In order to avoid the overclosure of the universe by these nonthermally produced LSPs, an LSP with a large pair-annihilation cross section, like Higgsino- or Wino-like neutralino, is required, instead of the standard Bino-like neutralino. This reveals new cosmologically interesting parameter regions in various SUSY breaking models, which have not attracted much attention so far.

hep-ph↗

arXiv2002

Natural Gravitino Dark Matter and Thermal Leptogenesis in Gauge-Mediated Supersymmetry Breaking Models

We point out that there is no cosmological gravitino problem in a certain class of gauge-mediated supersymmetry-breaking (GMSB) models. The constant term in the superpotential naturally causes small mixings between the standard-model and messenger fields, which give rise to late-time decays of the lightest messenger fields. This decay provides an exquisite amount of entropy, which dilutes the thermal relics of the gravitinos down to just the observed mass density of the dark matter. This remarkable phenomenon takes place naturally, irrespective of the gravitino mass and the reheating temperature of inflation, once the gravitinos and messenger fields are thermalized in the early Universe. In this class of GMSB models, there is no strict upper bound on the reheating temperature of inflation, which makes the standard thermal leptogenesis the most attractive candidate for the origin of the observed baryon asymmetry in the present Universe.

hep-ph↗

arXiv2002

Baryogenesis and Gravitino Dark Matter in Gauge-Mediated Supersymmetry-Breaking Models

We discuss two cosmological issues in a generic gauge-mediated supersymmetry (SUSY)-breaking model, namely the Universe's baryon asymmetry and the gravitino dark-matter density. We show that both problems can be simultaneously solved if there exist extra matter multiplets of a SUSY-invariant mass of the order of the ``$μ$-term'', as suggested in several realistic SUSY grand-unified theories. We propose an attractive scenario in which the observed baryon asymmetry is produced in a way totally independent of the reheating temperature of inflation without causing any cosmological gravitino problem. Furthermore, in a relatively wide parameter space, we can also explain the present mass density of cold dark matter by the thermal relics of the gravitinos without an adjustment of the reheating temperature of inflation. We point out that there is an interesting relation between the baryon asymmetry and the dark-matter density.

hep-ph↗

arXiv2002

Non-thermal dark matter via Affleck-Dine baryogenesis and its detection possibility

The formation and late time decays of Q-balls are generic consequences of the Affleck-Dine (AD) baryogenesis. A substantial amount of the lightest supersymmetry (SUSY) particles (LSPs) are produced non-thermally as the decay products of these Q-balls. This requires a significantly large annihilation cross section of the LSP so as not to overclose the universe, which predicts a higgsino- or wino-like LSP instead of the standard bino LSP. We have reexamined the AD baryogenesis with special attention to the late-time decays of the Q-balls, and then specified the parameter regions where the LSPs produced by the Q-ball decays result in a cosmologically interesting mass density of dark matter by adopting several SUSY breaking models. This reveals new cosmologically interesting parameter regions, which have not attracted much attention so far. We have also investigated the prospects of direct and indirect detection of these dark matter candidates, and found that there is an intriguing possibility to detect them in various next generation dark matter searches.

hep-ph↗